Should we make New York City’s public-school system more like a successful shoe retailer? Well, it couldn’t make things any worse.

In a speech at The New School last week, City Council Speaker Christine Quinn suggested that education in New York can be improved if we “recommit to doing things better.” She continued, “I don’t know . . . how many of you are familiar with the online shoe company Zappos. Zappos is recognized as a standout in customer service. They’re known for being obsessive . . .

“Their operators are instructed to stay on the phone as long as it takes to get a customer what they need. The longest call has been logged in as 10 1/2 hours . . . If Zappos can bring that level of commitment and urgency when they’re dealing with shoes, the greatest city in the world should be able to do the same thing for our parents and children.”

This in a week when a strike left 150,000 children (many of them with special needs) without a way to get to school, and in which the city lost half a billion dollars because the teachers union wouldn’t agree on an evaluation system. Sorry, but customer service isn’t exactly the problem.

Go ahead. Spend 10 hours on the phone with a New York City parent. She’ll probably still want some quality control for teachers and a driver pulling in at the bus stop in the morning.

But Zappos actually does have some things to teach our officials. It is a big success — Amazon bought it for $1.2 billion in 2009. And a big part of its success is choice: different brands, different price points, different colors.

For shoe retailers, it’s pretty obvious that one size doesn’t fit all. The same is true for education, but New York parents who can’t afford private schools are stuck in a system where just 12 percent of black fourth-grade boys are proficient in reading. Where is the choice?

Mind you, Zappos is most famous for its free-return policy. If you’re not happy, send it back — without even a shipping charge. Women I know buy a dozen pairs of shoes at a time, then return all but one.

City parents sure don’t have that option. The four-year high-school-graduation rate is under 50 percent, but New York parents can’t demand a refund.

Companies that are popular with their customers don’t keep selling defective products. Mayor Bloomberg has closed 140 failing schools since taking over the school system in 2003, trying to discontinue the worst of the products. But at least two mayoral candidates — Public Advocate Bill de Blasio and former Comptroller Bill Thompson — have called for a moratorium on school closings.

Then there are the employees. Zappos regularly offers its workers $2,000 to quit, according to US News and World Report — “to make sure employees are here for more than a paycheck.” It would take a lot more than two grand for most New York teachers to give up the gig they have.

As Fred Siegel notes in Commentary, “From fiscal 2003 to 2011, the education budget . . . [saw] almost a 70 percent increase in inflation-adjusted dollars. Most of the money was paid out in 43 percent across-the-board teacher-salary increases.”

The city spends over $100 million a year paying teachers who actually don’t teach — their positions have been cut but they can’t be let go thanks to union rules.

Speaking of which: Facing an uncertain economy in 2008, Zappos had to lay off 8 percent of its workforce in one fell swoop. That’s a pretty unlikely outcome in the city schools. The Democratic candidates have been aggressively courting the endorsement of Mike Mulgrew, the president of the United Federation of Teachers.

Mulgrew recently bragged to The New York Times about his relationship with the candidates, “I just had a press conference with one, and I talked to another yesterday,” — at which point, the reporter notes, “the number for yet another contender appeared on his phone’s caller-ID screen.” He continued: “I guess I’m a popular guy.”